Method of setting flow coefficient and flow meter using the same

ABSTRACT

The present invention relates to a method of setting a flow coefficient used in a flow meter for measuring a flow rate of a fluid, and a flow meter having the flow coefficient which is set by the flow coefficient setting method. An object of the present invention is to provide a method for efficiently providing an optimal approximate line represented by a low-degree function such that flow coefficients including a number of data sets are within a predetermined error, and to provide a flow meter with a reduced error. In order to achieve the object, the present invention includes the steps of: obtaining an optimal approximate line using a number n of consecutive sets of data points (Xi, Yi); increasing or decreasing the number n so that the n sets of data points are all within a predetermined error Er with respect to the optimal approximate line; and setting a region. Thus, it is possible to easily and automatically set a flow coefficient using a personal computer, or the like, with high efficiency and good reproducibility.

TECHNICAL FIELD

The present invention relates to a method of setting a flow coefficientused in a flow meter for measuring a flow rate of a fluid.

BACKGROUND ART

A conventional flow meter will be described with reference to FIG. 21. Aflow velocity measurement device 2 for measuring a flow velocity of afluid, such as a thermal type flow sensor, is provided at a point in afluid pipe 1 where a fluid passes therethrough. The flow velocity (Vm)obtained by the flow velocity measurement device 2 is multiplied by across-sectional area (S) of the fluid pipe 1 and a flow coefficient (K),so as to calculate a flow rate (Qm). The flow velocity measurementdevice 2 obtains the flow velocity (Vm) of the fluid by measuring theflow velocity of only a portion of the fluid in the vicinity of the flowvelocity measurement device 2. Therefore, an average flow velocity forthe entire area of the fluid pipe 1 needs to be calculated as follows. Areference flow rate setting section capable of setting a reference flowrate is connected to the fluid pipe 1 so as to pass a fluid at anappropriate reference flow rate through the fluid pipe 1 and obtain anaverage flow rate (Qa). Then, the relationship (K=Va/Vm; “flowcoefficient”) between an average flow velocity (Va), which is calculatedfrom the average flow rate value and the flow velocity (Vm) measured bythe flow velocity measurement device is obtained. This relationship ismeasured for various reference flow rates so as to obtain a number ofdata Bets each including the flow velocity (Vm) and the flow coefficient(K) of the fluid.

Next, the flow velocity (Vm) of the fluid measured by the flow velocitymeasurement device 2 is multiplied by the flow coefficient (K) and thecross-sectional area (S) of the fluid pipe 1, thereby obtaining ameasured flow rate (Qm). In other words, the measured flow rate (Qm) isobtained by calculating Qm=K·S·Vm. In FIG. 21, an arrow 3 denotes thedirection of the fluid flow. FIG. 22 illustrates a relationship betweenthe flow velocity (Vm) and the flow coefficient (K) which are obtainedas described above. In FIG. 22, the horizontal axis represents the flowvelocity (Vm) measured by the flow velocity measurement device, and thevertical axis represents the flow coefficient (K). For example, if theflow velocity (Vm) of the fluid measured by the flow velocitymeasurement device 2 is about 2 m/s, the flow coefficient (K) can beread from FIG. 22 to be about 0.89. Therefore, if the cross-sectionalarea (S) of the fluid pipe 1 is about 0.3×10⁻³ m², the measured flowrate (Qm) is: $\begin{matrix}{{Qm} = \quad {2 \times 0.89 \times 0.3 \times 10^{- 3}\quad m^{3}\text{/}s}} \\{= \quad {0.534 \times 10^{- 3}\quad m^{3}\text{/}s}} \\{= \quad {1.9\quad m^{3}\text{/}{h.}}}\end{matrix}$

The conventional flow meter has the following problems. That is, using anumber of sets of data (see FIG. 22) each including the flow velocity(Vm) and the flow coefficient (K) measured by the flow velocitymeasurement device, the flow velocity range is appropriately dividedinto regions by visual observation so as to set an optimal approximateline for each region which optimally approximates a group of data sets(flow coefficients) within the region, thereby obtaining a kinked linewhich optimally approximates the group of data sets (flow coefficients)across all regions.

It is time consuming and labor intensive to set such an optimalapproximate straight line by repeatedly performing complicatedcalculations. Moreover, because the setting operation is based on avisual observation, it has a poor reproducibility, and the obtainedoptimal approximate straight line may vary each time it is set. Althoughthe optimal flow coefficient may be approximated by a high-degree curve,a low-degree approximation such as a linear or quadric approximation ispreferred when the calculation is done by a microcomputer, or the like,because of the limitations associated with the use of a microcomputersuch as the calculation time and the number of significant digits.

When the type of a fluid is changed from that used when measuring thereference flow rate and setting the flow coefficient, it is necessary tore-measure the average flow rate (Qa) and the flow velocity (Vm) of thenew fluid so as to re-set a new flow coefficient (K).

When the temperature of the fluid changes, the characteristics of thefluid may also change, thereby changing the flow coefficient anddeteriorating the flow rate measurement precision.

DISCLOSURE OF THE INVENTION

The present invention has been made to solve the above-describedproblems and provides a method of setting a flow coefficient, includingthe steps of: obtaining an optimal approximate line using a number n ofconsecutive sets of data points (Xi, Yi) of all flow velocity datapoints measured by a flow velocity measurement section, and referencedata stored in a reference data memory section; increasing or decreasingthe number n so that the n sets of data points are all within apredetermined error Er with respect to the optimal approximate linerperforming a calculation operation for setting a region by a flowcoefficient calculation section; and storing an obtained flowcoefficient in a flow coefficient memory section.

With such a structure, according to the flow coefficient setting methodof the present invention having such a structure, it is possible toeasily and automatically set a flow coefficient using a personalcomputer, or the like, with good reproducibility, while suppressing theflow rate value within a predetermined error.

Another method of setting a flow coefficient of the present inventionincludes the steps of: obtaining an optimal approximate curve using aplurality of sets of data points (Xi, Yi) of all flow velocity datapoints measured by a flow velocity measurement section, and referencedata stored in a reference data memory section, dividing the optimalapproximate curve into a number m of regions; performing a calculationoperation for approximating each region with an optimal approximatestraight line by a flow coefficient calculation section; and storing anobtained flow coefficient in a flow coefficient memory section.

With such a structure, even if the number of data points available islimited, it is possible to select an optimal curve so that a flowcoefficient can be set with a reduced error over a wider range, in amore efficient manner and within a shorter period of time.

A flow meter of the present invention includes: a flow velocitymeasurement section for measuring a flow velocity of a fluid; a flowcoefficient memory section for storing a flow coefficient which is setby the above-described method of setting a flow coefficient; and a flowrate calculation section for calculating a flow rate of the fluid fromthe measured flow velocity using the flow coefficient stored in the flowcoefficient memory section.

With such a structure, it is possible to provide a flow meter with areduced error over a wide flow rate range.

Various embodiments of the present invention will be described below.

A method of setting a flow coefficient according to one embodiment ofthe present invention includes the steps of: obtaining an optimalapproximate line using a number n of consecutive sets of data points(Xi, Yi) of all flow velocity data points measured by a flow velocitymeasurement section, and reference data stored in a reference datamemory section; increasing or decreasing the number n so that the n setsof data points are all within a predetermined error Er with respect tothe optimal approximate line; performing a calculation operation forsetting a region by a flow coefficient calculation section; and storingan obtained flow coefficient in a flow coefficient memory section.

With such a structure, according to the flow coefficient setting methodof the present invention having such a structure, it is possible toeasily and automatically set a flow coefficient using a personalcomputer, or the like, with good reproducibility, while suppressing theflow rate value within a predetermined error.

In a method of setting a flow coefficient according to one embodiment ofthe present invention, a linear function is used to represent theoptimal approximate line if the n sets of data points (Xi, Yi) aredistributed on both sides of the optimal approximate line in a middleportion of the optimal approximate line.

With such a structure, it is possible to set a flow coefficient with asimple linear function and thus to obtain a flow rate value with areduced error by a a simple calculation.

In a method of setting a flow coefficient according to one embodiment ofthe present invention, a quadric function is used to represent theoptimal approximate line if the n sets of data points (Xi, Yi) aredistributed on one side of the optimal approximate line in a middleportion of the optimal approximate line.

With such a structure, it is possible to approximate a wider range, ascompared with when using a linear function, using a curve with a reducederror.

A method of setting a flow coefficient according to one embodiment ofthe present invention includes the steps of: obtaining an optimalapproximate curve using a plurality of sets of data points (Xi, Yi) ofall flow velocity data points measured by a flow velocity measurementsection, and reference data stored in a reference data memory section;dividing the optimal approximate curve into a number m of regions;performing a calculation operation for approximating each region with anoptimal approximate straight line by a flow coefficient calculationsection; and storing an obtained flow coefficient in a flow coefficientmemory section.

With such a structure, even if the number of data points available islimited, it is possible to select an optimal curve so that a flowcoefficient can be set with a reduced error over a wider range, in amore efficient manner and within a shorter period of time.

In a method of setting a flow coefficient according to one embodiment ofthe present invention, the optimal approximate curve is equally dividedinto the number m of regions along a y-axis direction.

With such a structure, it is possible to divide a data range into mregions along a y-axis direction within a shorter period of time,thereby efficiently setting a flow coefficient.

In a method of setting a flow coefficient according to one embodiment ofthe present invention, the optimal approximate curve is equally dividedinto the number m of regions along an x-axis direction.

With such a structure, it is possible to divide a data range into mregions along an x-axis direction within a shorter period of time,thereby efficiently setting a flow coefficient.

In a method of setting a flow coefficient according to one embodiment ofthe present invention, the optimal approximate curve is divided into thenumber m of regions along an x-axis direction such that a width of eachregion is inversely proportional to a gradient of the optimalapproximate straight line for the region.

With such a structure, it is possible to divide a data range into mregions within a shorter period of time, while efficiently setting aflow coefficient so that the errors of the respective regions are closeto one another.

In a method of setting a flow coefficient according to one embodiment ofthe present invention, the optimal approximate curve is represented byY=a×Log(X)+b.

With such a structure, it is possible to divide a setting range into mregions to linearly approximate each region with as few as two datapoints.

In a method of setting a flow coefficient according to one embodiment ofthe present invention, the optimal approximate curve is represented byY=(a−b)/[1+exp(−c×X)]+b.

With such a structure, it is possible to divide a wide setting rangeinto n regions to linearly approximate each region with a small numberof data points.

In a method of setting a flow coefficient according to one embodiment ofthe present invention, the flow velocity measurement section includes athermal type flow sensor.

With such a structure, it is possible to set a flow coefficient with areduced error and a good reproducibility particularly in a low flow rateregion.

In a method of setting a flow coefficient according to one embodiment ofthe present invention, the flow velocity measurement section includes anultrasonic flow meter.

With such a structure, it is possible to set a flow coefficient with areduced error and a good reproducibility over a wide flow rate range.

In a method of setting a flow coefficient according to one embodiment ofthe present invention, the optimal approximate line is represented by alow-degree function which is a linear function or a quadric function.

With such a structure, it is possible to obtain a flow rate value with areduced error by a simple calculation.

In a method of setting a flow coefficient according to one embodiment ofthe present invention, a data point which is included by two adjacentregions is set to belong to one of the two adjacent regions in which anerror Er calculated based on the optimal approximate line is smaller.

With such a structure, it is possible to reduce the error for a boundaryvalue.

In a method of setting a flow coefficient according to one embodiment ofthe present invention, an intersection between two optimal approximatelines for two adjacent regions is used as a boundary point between thetwo regions.

With such a structure, it is possible to smoothly connect the regionboundary points to one another.

In a method of setting a flow coefficient according to one embodiment ofthe present invention, the error Er is gradually increased until anentire data range required can be divided into a predetermined number ofregions.

With such a structure, even when the number of regions is prescribed, itis possible to divide a data range into the prescribed number of regionswhile setting a flow coefficient with a minimum error.

In a method of setting a flow coefficient according to one embodiment ofthe present invention, when a type of a fluid changes from a first fluidto a second fluid, an x-axis value of a flow coefficient is multipliedby a fluid-type-dependent constant so as to convert the flow coefficientto a new flow coefficient.

With such a structure, even when the type of a fluid changes from thatused when setting a flow coefficient, the flow coefficient can easily beconverted to a new flow coefficient for the new fluid, therebysuppressing an error which may be caused by such a change in the type ofa fluid.

In a method of setting a flow coefficient according to one embodiment ofthe present invention, the constant is a new flow velocity (Vm×Vg/Vm)which is obtained by multiplying a flow velocity ratio (Vg/Vm) to a flowvelocity (Vm) of the first fluid, where Vg is a flow velocity of thesecond fluid for any flow coefficient value (Kc).

With such a structure, even when there is a change in the type of afluid, it is possible to update the flow coefficient using only one datapoint according to the type a of the fluid, thereby eliminating the needto re-measure the flow coefficient.

In a method of setting a flow coefficient according to one embodiment ofthe present invention, when a temperature of a fluid changes from afirst temperature to a second temperature, an x-axis value of a flowcoefficient is multiplied by a temperature-dependent function value soas to convert the flow coefficient to a new flow coefficient.

With such a structure, even when the temperature of the fluid changesfrom that when setting a flow coefficient, the flow coefficient caneasily be converted to a new flow coefficient for the new temperature,thereby suppressing an error which may be caused by such a change in thetemperature of the fluid.

In a method of setting a flow coefficient according to one embodiment ofthe present invention, the function value used for obtaining the newflow coefficient is calculated by the following expression:

Vi(Ts/Ti)^(p)

where Ts denotes the first temperature, Ti denotes the secondtemperature, Vi denotes a flow velocity of the fluid measured at Ti, andp denotes an exponent.

With such a structure, even when there is a change in the temperature ofa fluid, it is possible to obtain a flow coefficient for the newtemperature, thereby suppressing an error which may be caused by such achange in the temperature of the fluid.

In a method of setting a flow coefficient according to one embodiment ofthe present invention, an absolute temperature (Tm) of the fluid isdetermined from a temperature-sensitive resistor of a thermal type flowsensor.

With such a structure, it is not necessary to separately provide atemperature sensor, thereby realizing an efficient setting method.

In a method of setting a flow coefficient according to one embodiment ofthe present invention, an absolute temperature (Tm) of the fluid isdetermined from an ultrasonic wave propagation time from an ultrasonicflow meter.

With such a structure, it is not necessary to separately provide atemperature sensor, while realizing an accurate hydraulic temperaturemeasurement utilizing the characteristics of a fluid.

A flow meter according to one embodiment of the present inventionincludes: a flow velocity measurement section for measuring a flowvelocity of a fluid; a flow coefficient memory section for storing aflow coefficient which is set by the above-described method of setting aflow coefficient; and a flow rate calculation section for calculating aflow rate of the fluid from the measured flow velocity using the flowcoefficient stored in the flow coefficient memory section.

With such a structure, it is possible to provide a flow meter with areduced error over a wide flow rate range.

In a flow meter according to one embodiment of the present invention,the flow velocity measurement section includes a thermal type flowsensor.

With such a structure, it is possible to provide a flow meter with areduced error and with good reproducibility particularly in a low flowrate region.

In a flow meter according to one embodiment of the present invention,the flow velocity measurement section includes an ultrasonic flow meter.

With such a structure, it is possible to provide a flow meter with areduced error and with good reproducibility over a wide flow rate range.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a conceptual diagram of a flow meter for illustratingEmbodiment 1 of the present invention;

FIG. 2 shows a flow velocity measurement section including a thermaltype flow sensor according to Embodiment 1 of the present invention;

FIG. 3 is a flow velocity measurement section including ultrasonictransceivers according to Embodiment 1 of the present invention:

FIG. 4 is a characteristic diagram showing a flow coefficient forillustrating Embodiment 1 of the present invention;

FIG. 5 is a characteristic diagram showing a flow coefficient forillustrating Embodiment 1 of the present invention;

FIG. 6 is a characteristic diagram showing a flow coefficient forillustrating Embodiment 1 of the present invention;

FIG. 7 is a characteristic diagram showing a flow coefficient forillustrating Embodiment 1 of the prevent invention;

FIG. 8 is a characteristic diagram showing a flow coefficient forillustrating Embodiment 2 of the present invention;

FIG. 9 is a characteristic diagram showing a flow coefficient forillustrating Embodiment 3 of the present invention;

FIG. 10 is a characteristic diagram showing a flow coefficient forillustrating Embodiment 4 of the present invention;

FIG. 11 is a characteristic diagram showing a flow coefficient forillustrating Embodiment 5 of the present invention;

FIG. 12 is a characteristic diagram showing a flow coefficient forillustrating Embodiment 6 of the present invention;

FIG. 13 is a characteristic diagram showing a flow coefficient forillustrating Embodiment 7 of the present invention;

FIG. 14 is a characteristic diagram showing a flow is coefficient forillustrating Embodiment 8 of the present invention;

FIG. 15 is a characteristic diagram showing a flow coefficient forillustrating Embodiment 8 of the present invention;

FIG. 16 is a characteristic diagram showing a flow coefficient forillustrating Embodiment 8 of the present invention;

FIG. 17 is a characteristic diagram showing a flow coefficient forillustrating Embodiment 9 of the present invention;

FIG. 18 is a characteristic diagram showing a flow coefficient forillustrating Embodiment 10 of the present invention;

FIG. 19 is a characteristic diagram showing a flow coefficient forillustrating Embodiment 11 of the present invention;

FIG. 20 is a diagram showing a structure of a flow meter forillustrating Embodiment 16 of the present invention;

FIG. 21 is a diagram showing a flow velocity measurement section forillustrating a conventional example; and

FIG. 22 is a characteristic diagram showing a flow coefficient forillustrating a conventional example.

BEST MODE FOR CARRYING OUT THE INVENTION

(Embodiment 1)

FIG. 1 is a conceptual diagram showing a flow meter for illustrating amethod of setting a flow coefficient according to Embodiment 1 of thepresent invention. Referring to FIG. 1, the flow meter includes: a flowvelocity measurement section 4 including a thermal type flow sensor oran ultrasonic transceiver; a reference data memory section 5 for storinga reference flow rate of a fluid; a flow velocity data memory section 6for storing flow velocity data measured by the flow velocity measurementsection 4; a flow coefficient calculation section 7 for calculating aflow coefficient; and a flow coefficient memory section 8 for storing acalculated flow coefficient.

Reference flow rate data of a fluid flowing through the flow velocitymeasurement section 4 is stored in the reference flow rate data memorysection 5. A measured flow velocity of the fluid flowing through theflow velocity measurement section 4 is stored in the flow velocity datamemory section 6. The flow coefficient calculation section 7 calculatesa flow coefficient using the reference flow rate data stored in thereference flow rate data memory section 5 and the flow velocity data ofthe fluid stored in the flow velocity data memory section 6. Thecalculation results are stored in the flow coefficient memory section 8.

FIG. 2 shows a flow velocity measurement section which includes athermal type flow sensor as a flow velocity measurement device. FIG. 3shows another flow velocity measurement section which includesultrasonic transceivers as a flow velocity measurement device.

Referring to FIG. 2, a thermal type flow sensor 10 is provided at apoint in a fluid pipe 9 as a flow velocity measurement device. Thethermal type flow sensor 10 includes a temperature-sensitive resistorand a heater element. An electric power is momentarily provided from anexternal unit to the heater element. Then, the thermal equilibriumbetween the heating of the temperature-sensitive resistor by the heaterelement and the cooling of the temperature-sensitive resistor by thefluid is measured as a resistance value of the temperature-sensitiveresistor, and converted to the flow velocity of the fluid. In this case,the flow velocity (Vm) of the fluid measured by the flow velocitymeasurement device represents the flow velocity of a portion of thefluid in the vicinity of the flow velocity measurement device. If thetemperature-sensitive resistor is appropriately calibrated in advance,it is possible to measure the temperature of the fluid from the changein the resistance value.

Referring to FIG. 3, ultrasonic transceivers 12 and 13 as a flowvelocity measurement device are provided along a fluid pipe 11respectively on the upstream side and the downstream side with respectto each other. An ultrasonic wave is transmitted from the upstreamultrasonic transceiver 12 to the downstream ultrasonic transceiver 13,and vice versa, so as to measure the propagation time of the ultrasonicwave for each direction. The flow velocity of the fluid is measured bythe difference between the respective propagation times. In FIG. 3, abroken line 14 denotes the propagation direction of the ultrasonicwaves, and a one dot chain line 15 and an arrow 16 both denote thedirection of the fluid flow. Reference numeral 17 (θ) denotes an anglebetween the propagation direction of the ultrasonic waves and thedirection of the fluid flow. In this case, the ultrasonic transceiversas a flow velocity measurement device measure the flow velocity (Vm) asan average flow velocity of the fluid along the propagation direction 14of the ultrasonic waves.

The above-described operation can be mathematically expressed asfollows:

Tud=L/(Vs+Vm×cos(θ)):

and

Tdu=L/(Vs−Vm×cos(θ))

where: Tud denotes the time required for an ultrasonic wave transmittedfrom the upstream ultrasonic transceiver 12 to be received by thedownstream ultrasonic transceiver 13; Tdu denotes the time required foran ultrasonic wave transmitted from the downstream ultrasonictransceiver 13 to be received by the upstream ultrasonic transceiver 12;L denotes the distance between the ultrasonic transceivers 12 and 13; Vsdenotes the sound velocity; and Vm denotes the flow velocity of thefluid.

Thus,

Vs+Vm×cos(θ)=L/Tud,

and

Vs−Vm×cos(θ)=L/Tdu.

The sum of the two expressions and the difference therebetween arerespectively as follows:

2×Vs=(L/Tud)+(L/Tdu);

and

2×Vm×cos(θ)=(L/Tud)−(L/Tdu).

Thus,

Vs=(L/2)×{(1/Tud)+(1/Tdu)};

and

Vm={L/(2×cos(θ))}×{(1/Tud)−(1/Tdu)}.

As can be seen from the above, the sound velocity Vs can be calculatedbased on the distance L between the ultrasonic transceivers and the sumof the respective inverse numbers of the propagation times Tud and Tdu.The flow velocity Vm can be calculated based on the distance, L betweenthe ultrasonic transceivers and the difference between the respectiveinverse numbers of the propagation times Tud and Tdu.

FIG. 4 shows a relationship between the flow velocity (Vm) of the fluidand the flow coefficient (K) measured as described above, for a numberof data sets (Vm, K). These sets of data are stored in the referencedata memory section 5 and the flow velocity data memory section 6.

FIG. 4 shows the flow velocity (Vm) of the fluid measured by the flowvelocity measurement device along the horizontal axis, and the flowcoefficient (K) along the vertical axis. As described above, the flowcoefficient (K) can be calculated as X=Va/Vm. Herein, the average flowvelocity (Va) can be calculated as Va=Qa/S (where, Qa denotes thereference flow rate, and S denotes the cross-sectional area of the fluidpipe), Thus, the reference flow rate (Qa) can be expressed asQa=S×Va=S×K×Vm.

Next, a method of setting the flow coefficient (K) used in the flowcoefficient calculation section 7 according to the present inventionwill be described. First, any number (e.g., five) of consecutive sets ofdata (Vm, K) (17, 18, 19, 20 and 21 in FIG. 4) are selected. Then, anoptimal approximate straight line 22, which gives the flow rateconversion coefficient (K), is calculated by a method such as a leastsquare method.

The optimal approximate straight line 22 is a straight line which givesa flow coefficient for a flow velocity value (Vm) measured by the flowvelocity measurement device. The optimal approximate straight line 22can be expressed by the following expression:

Kc=A×Vm+B

where A and B denote the gradient and the intercept of the line,respectively.

An error of each of the selected five data sets with respect to theoptimal approximate straight line 22 is calculated, and it is determinedwhether the error is within a predetermined range of error Er, e.g.,0.5%. In particular, the measured flow velocity Vm is applied to theoptimal approximate straight line 22 (Kc=A×Vm+B) so as to calculate anapproximated flow coefficient (Kc). The calculated flow coefficient (Kc)is compared with the measured flow coefficient (K) so as to obtain theerror therebetween.

If all of the data sets (the five data sets in this example) are withinthe error Er (0.5%), a new data set 23 is added thereto, as illustratedin FIG. 5, thereby increasing the number of data sets to six. In thesame manner as described above, another optimal approximate straightline 24, which gives the flow coefficient (K), is obtained by a leastsquare method using these six sets of data. It is determined whether allof the six data sets are within the error Er with respect to the optimalapproximate straight line 24. In the illustrated example, one of the sixdata sets (e.g., the data set 20) has an error greater than Er. Thus, inthis example, the highest possible number of consecutive data setswithin the predetermined error Er is five. Thus, a first regionincluding the five data sets 17, 18, 19, 20 and 21 is set.

Next, starting from the last data set 21 in the first region, any numberof data sets (21, 23, 25, 26, . . . ) are selected. Then, as describedabove, an optimal approximate straight line is calculated by a leastsquare method, and it is determined whether the data sets are within theerror Er. Thus, in the manner as described above, a second region is setwhich satisfies the error Er. For example, if six, and no mote, datasets 21, 23, 25, 26, 27 and 28 are within the error Er, the secondregion is determined to include the six data sets, thereby obtaininganother optimal approximate straight line 29. This is shown in FIG. 6.In this case, the data set 21 is a boundary point between the tworegions. Thereafter, further regions are set in this manner. When thesetting operation is complete, a flow coefficient given by the optimalapproximate straight line is within the predetermined error Er in eachregion.

FIG. 7 illustrates the obtained optimal approximate straight lineincluding a plurality of regions. The optimal approximate line includinga plurality of regions 30-39, which gives the flow coefficient, isstored in the flow coefficient memory section. The first region 30includes five data sets and the optimal approximate straight linetherefor is denoted by reference numeral 22. The second region 31includes six data sets and the optimal approximate straight linetherefor is denoted by reference numeral 32. The third region 33includes seven data sets and the optimal approximate straight linetherefor is denoted by reference numeral 34. The fourth region 35includes four data sets and the optimal approximate straight linetherefor is denoted by reference numeral 36. The fifth region 37includes four data sets and the optimal approximate straight linetherefor is denoted by reference numeral 38. The sixth region 39includes six data sets and the optimal approximate straight linetherefor is denoted by reference numeral 40.

When using the above-described method by applying it to a part of theregions, an upper limit value or a lower limit value can be set, so thatthe setting operation can be performed in one direction toward the upperlimit value or toward the lower limit value from one data set. In such acase, it is possible to perform the setting operation more efficientlyand thus to save time.

(Embodiment 2)

FIG. 8 shows a relationship between the flow velocity (Vm) and the flowcoefficient (K) for one region stored in the flow coefficient memorysection. In FIG. 8, reference numeral 40 denotes an optimal approximateline, 41 denotes another optimal approximate line 0.5% higher than theoptimal approximate line 40, 42 denotes another optimal approximate line0.5% lower than the optimal approximate line 40, 43 denotes the upperlimit of the region, and 44 denotes the lower limit of the region. Inthis case, the relationship between the measured flow velocity (Vm) andthe flow coefficient (K) is distributed within a range of ±0.5% withrespect to the optimal approximate line 40 represented by a linearfunction. Thus, an optimal approximate line represented by a linearfunction is sufficient for approximating the obtained data points.

(Embodiment 3)

FIG. 9 shows a relationship between the flow velocity (Vm) and the flowcoefficient (K) for another region stored in the flow coefficient memorysection. In FIG. 9, reference numeral 45 denotes an optimal approximateline, 46 denotes another optimal approximate line 0.5% higher than theoptimal approximate line 45, 47 denotes another optimal approximate line0.5% lower than the optimal approximate line 45, 48 denotes the upperlimit of the region, and 49 denotes the lower limit of the region. Inthis case, the relationship between the measured flow velocity (Vm) andthe flow coefficient (K) is distributed in a bell curve-like pattern. Inparticular, data points in the middle portion of the region representedby a linear function (between 48 and 49), are shifted toward the upperside of the optimal approximate line 45. On the other hand, data pointsnear the upper limit 48 and those near the lower limit 49 are shiftedtoward the lower side of the optimal approximate line 45. In this case,if an optimal approximate line is represented by a bell-shaped quadriccurve 50, the data points are more closely approximated by the optimalapproximate quadric curve.

Thus, where the data sets in the middle portion of the region areshifted to one side of the optimal approximate straight line, it is moreeffective to represent the optimal approximate line by a quadricfunction rather than a linear function, so that the error can be reducedand/or a greater range can be set as one region, thereby making thesetting operation efficient.

(Embodiment 4)

Next, another method of setting a flow coefficient will be described.

FIG. 10 shows a relationship between the measured flow velocity (Vm) andthe flow coefficient (K), for a number of data sets (Vm, K). These setsof data are stored in the reference data memory section 5 and the flowvelocity data memory section 6.

First, using all of the data sets (Vm, K) in FIG. 10, the flowcoefficient calculation section 7 calculates by a least square method,or the like, an optimal approximate function which gives the flowcoefficient K. The optimal approximate function may be, for example, afifth degree curve: Y=a₅×X⁵+a₄×X⁴+a₃×X³+a₂×X²+a₁×X¹+a₀×X⁰. The optimalapproximate curve is denoted by a solid line 51 in FIG. 10. Apredetermined flow velocity range is divided into a predetermined numbern of regions. Each region is linearly approximated by using a valuealong the obtained solid line 51 as a flow coefficient true value. Inthis way, even at a point between two measured data points, where therein no measured value, the flow coefficient (K) can be calculated from aflow velocity (Vm) using the fifth degree curve 51. Thus, it is possibleto more accurately obtain an approximate straight line.

The optimal approximate line calculated as described above is stored inthe flow coefficient memory section 8.

As can be seen from the above fifth degree expression, obtaining a fifthdegree curve requires only six data points (or six unknowns was, “a₅,a₄, a₃, a₂, a₁ and a₀”). Accordingly, obtaining a quartic curve requiresfive data points, and obtaining a cubic curve requires four data points.Thus, in the manner as described above, a wide range can be covered witha small number of data points. Moreover, if a tendency is known inadvance, the flow coefficient can be set more efficiently by determiningthe relationship between the flow velocity (Vm) and the flow coefficient(K) according to the degree of the optimal approximate line.

(Embodiment 5)

Next, a method of dividing a given flow velocity range into n regionswill be described. FIG. 11 shows a case where the flow velocity (Vm)range is divided into five regions. More specifically, the flow velocity(Vm) range is divided into the following five regions: 0-1.3, 1.3-2.6,2.6-3.9, 3.9-5.2 and 5.2-6.5. For each of the boundary Vm values, theflow coefficient (K) is calculated by using the fifth degree curve 51.The calculated boundary points are linked to one another by straightlines. The straight lines (denoted by five solid lines 52, 53, 54, 55and 56, respectively, in FIG. 11) are used as flow coefficientapproximate straight lines. For the solid line 52, for example, the datasets at the opposite ends thereof are calculated from the fifth degreecurve 51 shown in FIG. 10, thereby obtaining two data sets (Vm, K): (0,0.65) and (1.3, 0.87). Then, the flow coefficient (K) can be expressedby the following expression: K=0.16×Vm+0.65. As described above, even apoint where there is no measured data can easily be calculated. Thus, anapproximate straight line can easily be set.

(Embodiment 6)

Next, another n-division method will be described. FIG. 12 shows a casewhere the flow coefficient (K) range is divided into three regions. Morespecifically, the flow coefficient (K) range to divided into thefollowing three regions: 0.65-0.77, 0.77-0.88 and 0.88-0.95. For each ofthe boundary flow coefficients (K), a data set corresponding to theboundary point is calculated. The calculated data points are linked toone another by straight lines. The straight lines (denoted by threesolid lines 57, 58 and 59, respectively, in FIG. 12) are used as flowcoefficient approximate straight lines for the respective regions.

As in Embodiment 5, even a point where there is no measured data caneasily be calculated. Thus, an approximate straight line can easily beset. The set approximate straight lines for calculating the flowcoefficient (K) are stored in the flow coefficient memory section.

In the setting method of Embodiment 5, an upper limit value or a lowerlimit value is preferably provided for the flow velocity (Vm) (or forthe flow coefficient (K) for Embodiment 6), so that the settingoperation can be performed more efficiently. In this way, the settingoperation can be performed more efficiently within a shorter period oftime, particularly when applying the present invention to a flow meter,or the like, where the required range, the flow velocity range or theflow coefficient range is often prescribed.

(Embodiment 7)

Next, still another n-division method will be described. In thisEmbodiment, the width of each region (the width along the x axis) is setto be inversely proportional to the gradient of the approximate line soas to improve the proximity to the flow coefficient (K). In this way,the width along the x axis is smaller for a region where the gradient islarger, and the width along the x axis is larger for a region where thegradient is smaller. As a result, the proximity of the approximatestraight line which depends upon the gradient becomes more uniformacross all regions. FIG. 13 shows a case where a data range is dividedinto five regions in such a manner. More specifically, the data range isdivided into the following five regions: 0.65-0.73, 0.73-0.83,0.83-0.88, 0.88-0.93 and 0.93-0.98 in terms of the flow coefficient (K).In the figure, the respective approximate straight lines are denoted byfive solid lines 60, 61, 62, 63 and 64. As described above, even for apoint where there is no measured data, a data set corresponding to aboundary value can easily be calculated using, the fifth-degree curve.Thus, an approximate straight line can easily be set. The setapproximate straight lines for calculating the flow coefficient (K) arestored in the flow coefficient memory section.

(Embodiment 8)

Next, referring to FIG. 14, a further n-division method will bedescribed in which the proximity to the flow coefficient is furtherimproved so an to better suppress the error within the predeterminederror Er. FIG. 14 shows a fifth degree curve 51 obtained by measureddata sets (Vm, K). More particularly, FIG. 14 shows a case where thesetting operation starts from an upper limit value 65 (indicated by thesymbol “∘”), using the fifth degree curve 51 as a flow coefficient truevalue with the error Er being predetermined to be 2%, for example. Anypoint, e.g., a point 66 (also indicated by the symbol “∘”), is selectedalong the fifth degree curve 51 at a flow velocity (Vm) smaller thanthat at the point 65. Referring to an enlarged view shown in FIG. 15,the points 65 and 66 are linked to each other by a straight line(indicated by a broken line 67). The straight line 67 is assumed to bean approximate straight line which gives the flow coefficient (K). Sincethe straight line 67 passes through the two points 65 and 66 along thefifth degree curve 51, the coordinates (Vm, K) of the two points 65 and66 can easily be calculated using the fifth degree expression shownabove. Accordingly, the expression which represents the straight line 67passing through the two points 65 and 66 can also be calculated easily.

Then, for a selected flow velocity Vm between the points 65 and 66, theflow coefficient (K) is calculated. In particular, the true value of theflow coefficient (K) is calculated using the fifth degree curve 51.Moreover, for the flow velocity Vm, an approximate value (Kc) of theflow coefficient is also calculated using the straight line 67. Thecalculated approximate value (Kc) is compared with the true value (K) soas to calculate the error therebetween. If the error is within thepredetermined error Er (2%), the point 66 is slightly moved to a smallerflow velocity (Vm) (i.e., to the left in FIG. 15), and theabove-described operation is repeated. If the calculated error isgreater than the predetermined error Er (2%), the point 66 is slightlymoved to a larger flow velocity (Vm) (i.e., to the right in FIG. 25),and the above-described operation is repeated. The amount by which thepoint 66 is moved each time is dependent upon the required precision. Inthe present Embodiment, the amount is set to 0.001.

FIG. 16 shows the results of the operation as described above Referringto FIG. 16, five approximate straight lines (indicated by broken lines67, 68, 69, 70 and 71) are set starting from the upper limit value 65(indicated by the symbol “∘”), wherein the error is within the error Er(2% for each of the approximate straight lines. Thus, the predeterminedflow velocity (Vm) range is divided into five regions. The obtainedresults show that any point along the fifth degree curve 51 has an errorwithin 2% as calculated using these approximate straight lines. The setapproximate straight lines for calculating the flow coefficient (K) arestored in the flow coefficient memory section.

(Embodiment 9)

Still another n-division method will be described, which is similar toEmbodiment 8 but is more suitable where the maximum number of regions,i.e., the maximum number of approximate straight lines, is limited. Forexample, the maximum number of approximate straight lines (regions) isassumed to be three. The setting operation as shown in Embodiment 8 isperformed with the error Er being predetermined to be 2%, therebyresulting in five approximate straight lines (regions). Since this isover the maximum number of regions available (i.e., three), thepredetermined error Er is gradually increased, e.g., to 2.5%, 3.0%, andso forth, and the setting operation as shown in Embodiment 8 isrepeated. In this manner, three approximate straight lines (regions)with an optimal error distribution across all regions can be obtained.

When the maximum number of approximate straight lines is as large asten, on the other hand, the predetermined error Er can be graduallydecreased, e.g., to 1.5%, 0.5%, and so forth, thereby obtaining tenapproximate straight lines (regions) with an optimal error distributionacross all regions. For the data shown in FIGS. 14 to 16, the number ofapproximate straight lines is nine with the error Er being 0.5%. In thisway, an optimal error distribution can be obtained for any particularnumber of approximate straight lines. The set approximate straight linesfor calculating the flow coefficient (K) are stored in the flowcoefficient memory section.

(Embodiment 10)

Next, a function form other than the fifth degree curve which can beused as a true value of the flow coefficient (K) will be described. Ithas been found that with the arrangement of the flow velocitymeasurement section as illustrated in FIGS. 2 and 3, the followingfunction form exhibits a higher proximity than a fifth degree function.

Y=a×Log(X)+b

where X denotes the flow velocity (Vm), and Y denotes the flowcoefficient (K).

FIG. 17 shows a solid line 72 obtained by the above expression wherea=0.067 and b=0.299. It can be seen from FIG. 17 that the solid line 72is a good approximate curve in the wide range of flow velocity (Vm) from0.2 to 6.0. In this case, since there are only two unknowns (a and b),the above expression can be calculated only with two measured datapoints so as to calculate an approximate curve over a wide range. Thus,it is also possible to calculate an approximate straight line bycalculating the above expression from two data sets (Vm, K) and usingthe calculated value as a flow coefficient true value. Thus, theoperation efficiency is considerably improved. In Embodiment 10, theabove-described function form is applied to all of the regions.Alternatively, the setting operation can efficiently be performed bypartially applying it to some of the regions.

(Embodiment 11)

Next, still another function form will be described. It has been foundthat with the arrangement of the flow velocity measurement section asillustrated in FIGS. 2 and 3, if a rectification section is providedalong the pipe upstream of the flow velocity measurement section, theflow coefficient (K) tends to approach a constant value in a low flowvelocity region and in a high flow velocity region. In such a case, thefunction form represented by the following expression exhibits a higherproximity than that described in Embodiment 10.

Y=(a−b)/[1+exp(−cX)]+b

where X denotes the flow velocity (Vm), Y denotes the flow coefficient(K), and a, b and c are unknowns,

Herein, the unknown b denotes a constant value in the low flow velocityregion, i.e., a lower limit value of the flow coefficient. The unknown adenotes a constant value in the high flow velocity region, i.e., anupper limit value of the flow coefficient. FIG. 18 shows the measuredflow coefficient values measured with the rectification section providedon the upstream side, and the calculation result of the above expressionwhere a=0.920, b=0.385 and c=1.50. In FIG. 18, each symbol “⋄”represents a measured value, and a solid line 73 is a curve obtainedbased on the above expression. It can be seen that the above functionincluding the three unknowns a, b and c exhibits a good proximity over avery wide range. The above expression can be calculated with as few asthree data sets (Vm, K). Using the obtained value as a true value of theflow coefficient (K), it is possible to easily set an approximatestraight line to the flow coefficient (K) without having to measure manydata points.

Again, the set approximate straight lines for calculating the flowcoefficient (K) are stored in the flow coefficient memory section. Ithas also been confirmed that where the flow coefficient (K) exhibits anupward slant to the right in the high flow velocity region (i.e., wherethe flow coefficient (K) increases in proportion to the flow velocity),the constant a in the above function form can be substituted with d×X+eto obtain a good proximity to the measured values. In such a case,however, there is one additional unknown d. In Embodiment 11, theabove-described function form is applied to all of the regions.Alternatively, the setting operation can efficiently be performed bypartially applying it to some of the regions.

(Embodiment 12)

Next, how to handle a boundary point between two adjacent regions willbe discussed. The flow coefficients and the regions are set while usingsuccessive data sets. As a result, a data set corresponding to theboundary between two regions belongs to both of the regions. If the flowvelocity of the fluid measured by the flow velocity measurement sectioncoincides with a boundary flow velocity value, it is necessary todetermine whether the flow coefficient of one region or that of theother region is to be used for the measured flow velocity. According toEmbodiment 12, a boundary value between two adjacent regions is net sothat it belongs to one of the regions that gives a flow coefficient witha smaller error. As a result, it is possible to reduce the error for aboundary value.

(Embodiment 13)

Next, a method of setting a boundary value will be described. Anintersection between two low-degree optimal approximate lines which areset for two adjacent regions is used as the boundary value therebetween.

This method reduces a gap which may occur between two adjacent optimalapproximate lines, thereby more smoothly connecting the optimalapproximate lines with one another. Moreover, with this method, it ispossible to uniquely determine the boundary between two adjacentregions, and to realize at one-to-one correspondence between themeasured flow velocity (Vm) and the flow coefficient (K).

(Embodiment 14)

Another method of setting a flow coefficient suitable when a type of afluid whose flow rate is to be measured changes after setting a flowcoefficient (K). For example, assume a case where the flow coefficient(K) of air is first measured, thereby obtaining measured values (eachdenoted by the symbol “⋄” in FIG. 18) and setting a flow coefficient(represented by the solid line 73 in FIG. 18), after which the measuredfluid is changed to nitrogen, methane, propane, etc. Referring to FIG.18, for example, the change in the flow coefficient (K) for air for theflow velocity range of 0-7 m/s is about 0.65 to about 0.98. The midvalue between the flow coefficient values 0.65 and 0.98 is about K=0.80.Then, the flow velocity of the new fluid for K=0.80 is measured by aflow velocity measurement device, so as to calculate the flow velocityratio Rv therebetween by the following expression:

Rv=Vm(Gas, 0.80)/Vm(Air, 0.80)

where Vm(Gas, 0.80) denotes the flow velocity of the new fluid forK=0.80, and Vm(Air, 0.80) denotes the flow velocity of air measured forK=0.80.

Then, the measured flow velocity Vm(Air), which can be obtained fromFIG. 18, is multiplied by the flow velocity ratio Rv so as to obtain anew flow velocity. FIG. 19 shows the results by a two dot chain line 74.In the illustrated example, the flow velocity ratio Rv is about 2 toabout 3. The two dot chain line 74 obtained as described above denotesthe converted flow coefficient (K) for the new fluid (Gas). The solidline 73 in FIG. 19 denotes the flow coefficient (K) for air.

In this manner, the flow coefficient (K) can easily be re-calculatedeven when the measured fluid changes. Thus, it is possible to easilyobtain the flow coefficient for a new fluid (Gas) without having tonewly measure the flow coefficient (K) for the new fluid (Gas). In otherwords, it is possible to obtain a flow coefficient for a different fluidby changing (re-scaling, in this case) the flow velocity (Vm) accordingto the type of the fluid. As described above, any change in the measuredfluid can be accommodated simply by multiplying a constant, whichdepends upon the type of the fluid (i.e., the flow velocity ratio Rv) tothe horizontal axis value (Vm) of the flow coefficient (K) graph.

(Embodiment 15)

A method of setting a flow coefficient for a fluid suitable when thetemperature of the fluid, whose flow rate is to be measured, changesafter setting the flow coefficient (K) for a certain fluid at a certaintemperature will be described below. When the temperature of a fluidchanges, the characteristics of the fluid may also change, therebycausing an error in the measured flow rate value. The method ofEmbodiment 15 can provide a flow rate value with a reduced error evenwhen the temperature of the fluid changes.

For example, assume that the flow coefficient (K) as shown in FIG. 18 isfirst set at a temperature Ts (e.g., 20° C., 293.15 K, referencetemperature). When the temperature of the fluid changes (e.g., due to achange in the ambient temperature) to a new temperature Ti before theflow rate of the fluid is measured, some error may occur if thepredetermined flow coefficient (K) is used with the new temperature. Ithas been experimentally confirmed that it is possible to suppress theerror to a level which is practically not problematic (e.g., about 1.5%or less), as follows. First, the flow velocity Vi is measured at the newtemperature Ti. Then, the flow velocity Vi is converted to a new flowvelocity Vi₂ by the following expression:

Vi ₂ =Vi(Ts/Ti)^(p)

where Ts denotes the temperature of the fluid when setting the flowcoefficient (K), Ti denotes the temperature of the fluid when measuringthe flow rate of the fluid, Vi denotes the flow velocity of the fluidmeasured at the new temperature Ti, and p denotes an exponent to bedescribed below. Herein, the temperatures Ts and Ti are bothabsolute-temperatures [K].

Then, a flow coefficient Ki at the new temperature Ti obtained from FIG.18 as a flow coefficient value for the converted flow velocity Vi₂.Finally, the flow rate of the fluid is calculated based on the obtainedflow coefficient Ki.

Regarding the exponent p, it has been confirmed that the exponent pshould preferably be about 1.5 to about 3.0, and more preferably about2.5, the value which exhibited the best conformity to the experimentalvalues.

For example, assume a case where a flow coefficient (K) is met when thetemperature Ts of the fluid is 20° C. (293 K), after which the flowvelocity Vi of the same fluid is measured to be 2 m/s when thetemperature Ti of the fluid is 0° C. (273 K). At 20° C.; the flowcoefficient (K) for the flow velocity of 2 m/s can be read from FIG. 12to be about 0.89. However, the flow coefficient (K) should instead beobtained as follows since the temperature has changed to 0° C. First, byusing the above expression, the measured flow velocity Vi is convertedto Vi₂ as follows:

Vi ₂=2·(293/273){circumflex over ( )}2.5=2.38 m/s.

Then, the flow coefficient (Ki) for the fluid temperature of 0° C. canbe read from FIG. 18 to be about 0.91 (corresponding to Vm=2.38 m/sec).

Thus, even when the temperature of the fluid changes, the flowcoefficient value for the new temperature can be obtained by convertingthe solid line 73 in FIG. 18, i.e., the flow coefficient for the firsttemperature (20° C.), to another flow coefficient for the nowtemperature, thereby eliminating the need to newly measure the flowcoefficient for the new temperature and thus making the settingoperation very efficient. In other words, since the approximate straightline to the flow coefficient is set while using an optimal function, itis possible, even when the temperature of the fluid changes, tocalculate a new flow coefficient for the new temperature by a simplecoordinate conversion, i.e., by multiplying a temperature-dependentfunction value (e.g., the temperature ratio as in this case) to thex-axis value (flow velocity).

To measure the temperature of the fluid, a temperature sensor may beseparately provided in the fluid pipe. However, it may not be necessaryaccording to the present invention. For example, when the flow velocityof the fluid is measured by a thermal type flow sensor, since a thermaltype flow sensor includes a temperature-sensitive resistor, thetemperature of the fluid can easily be obtained by measuring theresistance value thereof.

Also when the flow velocity of the fluid is measured by a pair ofultrasonic transceivers which are provided along the fluid piperespectively on the upstream side and the downstream side with respectto each other), it is not necessary to separately provide a temperaturesensor for the following reason.

The distance L between the upstream ultrasonic transceiver and thedownstream ultrasonic transceiver is constant and known. Therefore,based on the average propagation time between the ultrasonictransceivers (i.e., the sum of the inverse number of the propagationtime from the upstream side to the downstream side and the inversenumber of the propagation time from the downstream side to the upstreamside), the sound velocity Vs through the measured fluid can be obtainedby the following expression:

Vs=(L/2)×{(1 /Tud)+(1/Tdu)}.

As can be seen, the sound velocity expression contains no term for theflow velocity of the fluid. This means that the sound velocity Vsthrough the measured fluid can be known independently of the flowvelocity of the fluid.

Since the velocity of sound propagating through a fluid is stronglydependent upon the temperature of the fluid, it is possible to obtainthe temperature of the fluid based on the sound velocity. As is commonlyknown, the sound velocity through air V(Air) m/s can be expressed asfollows by a linear function:

V(Air)=331.5+0.6×t,

or

 V(Air)=331.5+0.6×(Tabs−273.15)

where t denotes a temperature in Celsius (°C.), and Tabs denotes anabsolute temperature (K).

Since the temperature t of the fluid can easily be obtained from thesound velocity V(Air), as described above, it is not necessary in thepresent invention to separately provide the temperature sensor formeasuring the temperature of the fluid.

In Embodiment 15 described above, the temperature ratio of the fluid (inabsolute temperature) is used when converting the flow coefficient toaccommodate a change in the temperature of the fluid. However, a soundvelocity ratio of the fluid may alternatively be used instead of thetemperature ratio because the temperature of a fluid and the soundvelocity through the fluid are strongly correlated with each other, asdescribed above. In such a case, however, the exponent p may be slightlydifferent from that shown above.

(Embodiment 16)

A flow meter which uses a flow coefficient (K) obtained by the flowcoefficient setting method of the present invention will be describedwith reference to FIG. 20. Referring to FIG. 20, the flow meterincludes: a flow velocity measurement section 4 for measuring the flowvelocity of a fluid; a flow coefficient memory section 8 for storing aflow coefficient which is set as described above according to thepresent invention; a flow rate calculation section 75 for calculatingthe flow rate of the fluid using the flow velocity (Vm) measured by theflow velocity measurement section 4 and the flow coefficient (K) storedin the flow coefficient memory section 8; and an output section 76 foroutputting the calculated flow rate value (Qcal). When the flow velocitymeasurement section 4 measures the flow velocity of the fluid to be Vm,a flow coefficient (K) corresponding to the flow velocity Vm is obtainedfrom the flow coefficient memory section 8. Then, the flow ratecalculation section 75 performs a calculation Qcal=S×Vm×K, therebyobtaining the flow rate (Qcal) of the fluid. The calculation result isoutput to the output section 76 which includes a liquid crystal display,or the like.

As described above, the flow meter of the present invention includes theflow coefficient memory section 8 for storing the flow coefficient whichis set based on the flow coefficient setting method as described abovein detail. Thus, the flow meter of the present invention is capable ofoutputting a flow rate value with a reduced error. Even when the type ofa fluid changes from that used when setting the flow coefficient, theflow coefficient can easily be converted as described above, whereby theflow meter of the present invention is still capable of outputting aflow rate value with a reduced error. Moreover, also when thetemperature of the fluid changes, the flow coefficient can easily beconverted as described above, whereby the flow meter of the presentinvention is still capable of outputting a flow rate value with areduced error.

(Embodiment 17)

A flow meter of Embodiment 17 is similar to that described above inEmbodiment 16, but the flow velocity measurement section 4 in Embodiment17 employs a thermal type flow sensor. In other words, the flow velocitymeasurement section 4 has a structure as illustrated in FIG. 2. Withsuch a structure, it is possible to provide a flow meter having areduced error particularly in a low flow rate region. Moreover, thetemperature of the fluid can be directly measured from thetemperature-sensitive resistor of the thermal type flow sensor. Thus,the flow meter can be provided in a simpler structure without having toseparately provide a temperature sensor for measuring the temperature ofthe fluid.

(Embodiment 18)

A flow meter of Embodiment 18 is similar to that described above inEmbodiment 16, but the flow velocity measurement section 4 in Embodiment18 employs a pair of ultrasonic transceivers which are provided alongthe fluid pipe respectively on the upstream side and the downstream sidewith respect to the flow velocity measurement section. In other words,the flow velocity measurement section 4 has a structure as illustratedin FIG. 3. With such a structure, it is possible to provide a flow meterhaving a particularly reduced error over a wide flow rate range.Moreover, the temperature of the fluid can be directly measured based onthe sound velocity. Thus, the flow meter can be provided in a simplerstructure without having to separately provide a temperature sensor formeasuring the temperature of the fluid.

INDUSTRIAL APPLICABILITY

As is apparent from the above description, the flow coefficient settingmethod of the present invention first obtains a low-degree optimalapproximate line using an arbitrarily selected number of consecutivedata sets, and then selects (or adjusts) the number of data sets so asto select a highest possible number of data sets all within apredetermined error Er, thereby efficiently setting the optimalapproximate line.

Alternatively, a high-degree function representing an optimalapproximate curve may be obtained by using a number of data sets over awide range, after which a low-degree function representing an optimalapproximate line to flow coefficients is obtained based on the optimalapproximate curve. In such a case, it is possible to quickly andefficiently calculate the flow coefficients over a wide range using alimited number of data sets.

An alternative flow coefficient setting method of the present inventionconverts a flow coefficient for one type of a fluid to a new flowcoefficient for another type of a fluid by multiplying afluid-type-dependent constant to an x-axis value. Thus, even when thetype of a fluid changes from that used when setting a flow coefficient,the flow coefficient can easily be converted to a new flow coefficientfor the new fluid, thereby realizing a flow coefficient with a reducederror even when there is a change in the type of a fluid.

An alternative flow coefficient setting method of the present inventionconverts a flow coefficient for one temperature to a new flowcoefficient for another temperature by multiplying atemperature-dependent function value to an x-axis value. Thus, even whenthe temperature of the fluid changes from that when setting a flowcoefficient, the flow coefficient can easily be converted to a new flowcoefficient for the new temperature, thereby realizing a flowcoefficient with a reduced error even when there is a change in thetemperature of a fluid.

A flow meter using such a flow coefficient setting method can measurethe flow rate of a fluid with a reduced error over a wide range of flowrates.

What is claimed is:
 1. A method of setting a flow coefficient,comprising the steps of: obtaining an optimal approximate line of arelationship between the flow velocity of the fluid and the flowcoefficient using a number n of consecutive sets of data points (Xi, Yi)of all flow velocity data points stored in a flow velocity data memorysection for storing flow velocity data measured by a flow velocitymeasurement section, and reference data stored in a reference datamemory section; increasing or decreasing the number n so that the n setsof data points are all within a predetermined error Er with respect tothe optimal approximate line; performing a calculation operation forsetting a region by a flow coefficient calculation section; and storingan obtained flow coefficient in a flow coefficient memory section.
 2. Amethod of setting a flow coefficient according to claim 1, wherein alinear function is used to represent the optimal approximate line if then sets of data points (Xi, Yi) are distributed on both sides of theoptimal approximate line in a middle portion of the optimal approximateline.
 3. A method of setting a flow coefficient according to claim 1,wherein a guadric function is used to represent the optimal approximateline if the n sets of data points (Xi, Yi) are distributed on one sideof the optimal approximate line in a middle portion of the optimalapproximate line.
 4. A method of setting a flow coefficient, comprisingthe steps of: obtaining an optimal approximate curve of a relationshipbetween the flow velocity of the fluid and the flow coefficient using aplurality of sets of data points (Xi, Yi) of all flow velocity datapoints stored in a flow velocity data memory section for storing flowvelocity data measured by a flow velocity measurement section, andreference data stored in a reference data memory section; dividing theoptimal approximate curve into a number m regions; performing acalculation operation for approximating each region with an optimalapproximate straight line by a flow coefficient calculation section; andstoring an obtained flow coefficient in a flow coefficient memorysection.
 5. A method of setting a flow coefficient according to claim 4,wherein the optimal approximate curve is equally divided into the numberm of regions along a y-axis direction.
 6. A method of setting a flowcoefficient according to claim 4, wherein the optimal approximate curveis equally divided into the number m of regions along an x-axisdirection.
 7. A method of setting a flow coefficient according to claim4, wherein the optimal approximate curve is divided into the number m ofregions along an x-axis direction such that a width of each region isinversely proportional to a gradient of the optimal approximate straightline for the region.
 8. A method of setting a flow coefficient accordingto claim 4, wherein the optimal, approximate curve is represented byY=a×Log(X)+b.
 9. A method of setting a flow coefficient according toclaim 4, wherein the optimal approximate curve is represented byY=(a−b)/[1+exp(−c×X)]+b.
 10. A method of setting a flow coefficientaccording to claim 1 or 4, wherein the flow velocity measurement sectioncomprises a thermal type flow sensor.
 11. A method of setting a flowcoefficient according to claim 1 or 4, wherein the flow velocitymeasurement section comprises an ultrasonic flow meter.
 12. A method ofsetting a flow coefficient according to claim 1 or 4, wherein theoptimal approximate line is represented by a low-degree function whichis a linear function or a quadric function.
 13. A method of setting aflow coefficient according to claim 1 or 4, wherein a data point whichis included by two adjacent regions is set to belong to one of the twoadjacent regions in which an error Er calculated based on the optimalapproximate line is smaller.
 14. A method of setting a flow coefficientaccording to claim 1 or 4, wherein an intersection between two optimalapproximate lines for two adjacent regions is used as a boundary pointbetween the two regions.
 15. A method of setting a flow coefficientaccording to claim 1 or 4, wherein the error Er is gradually increaseduntil an entire data range required can be divided into a predeterminednumber of regions.
 16. A method of setting a flow coefficient accordingto claim 1 or 4, wherein when a type of a fluid changes from a firstfluid to a second fluid, an x-axis value of a flow coefficient ismultiplied by a fluid-type-dependent constant so as to convert the flowcoefficient to a new flow coefficient.
 17. A method of setting a flowcoefficient according to claim 16, wherein the constant is a new flowVelocity (Vm×Vg/m) which is obtained by multiplying a flow velocityratio (Vg/Vm) to a flow velocity (Vm) of the first fluid, where Vg is aflow velocity, of the second fluid for any flow coefficient value (Ko).18. A method of setting a flow coefficient according to claim 1 or 4,wherein when a temperature of a fluid changes from a first temperatureto a second temperature, an x-axis value of a flow coefficient ismultiplied by a temperature-dependent function value so as to convertthe flow coefficient to a new flow coefficient.
 19. A method of settinga flow coefficient according to claim 18, wherein the function valueused for obtaining the new flow coefficient is calculated by thefollowing expression: Vi(Ts/Ti)^(p) where Ts denotes the firsttemperature, Ti denotes the second temperature, Vi denotes a flowvelocity of the fluid measured at Ti, and p denotes an exponent.
 20. Amethod of setting a flow coefficient according to claim 19, wherein anabsolute temperature (Tm) of the fluid is determined from an ultrasonicwave propagation time from an ultrasonic flow meter.
 21. A method ofsetting a flow coefficient according to claim 18, wherein an absolutetemperature (Tm) of the fluid is determined from a temperature-sensitiveresistor of a thermal type flow sensor.
 22. A flow meter, comprising: aflow velocity measurement section for measuring a flow velocity of afluid; a flow coefficient memory section for storing a flow coefficientwhich is set by a method of setting a flow coefficient according toclaim 1 or 4; and a flow rate calculation section for calculating a flowrate of the fluid from the measured flow velocity using the flowcoefficient stored in the flow coefficient memory section.
 23. A flowmeter according to claim 22, wherein the flow velocity measurementsection comprises a thermal type flow sensor.
 24. A flow meter accordingto claim 22, wherein the flow velocity measurement section comprises anultrasonic flow meter.